svp factoriser les expressions suivantes a=x²+2x-15 b= x²+4x-32 c= x²-x-6 d= 4x²-4x-15
Mathématiques
tounnaaya86
Question
svp factoriser les expressions suivantes
a=x²+2x-15
b= x²+4x-32
c= x²-x-6
d= 4x²-4x-15
a=x²+2x-15
b= x²+4x-32
c= x²-x-6
d= 4x²-4x-15
1 Réponse
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1. Réponse loulakar
Bonjour
factoriser les expressions suivantes
a=x²+2x-15
a = x^2 + 2 * x * 1 + 1^2 - 1^2 - 15a = (x + 1)^2 - 1 - 15
a = (x + 1)^2 - 16
a = (x + 1)^2 - 4^2 => du type : a^2 - b^2
a = (x + 1 - 4)(x + 1 + 4)
a = (x - 3)(x + 5)
b= x²+4x-32B = x^2 + 2 * x * 2 + 2^2 - 2^2 - 32
B = (x + 2)^2 - 4 - 32
B = (x + 2)^2 - 36
B = (x + 2)^2 - 6^2
B = (x + 2 - 6)(x + 2 + 6)
B = (x - 4)(x + 8)
c=x²-x-6C = x^2 - 2 * x * (1/2) + (1/2)^2 - (1/2)^2 - 6
C = (x - 1/2)^2 - 1/4 - 24/4
C = (x - 1/2)^2 - 25/4
C = (x - 1/2)^2 - (5/2)^2
C = (x - 1/2 - 5/2)(x - 1/2 + 5/2)
C = (x - 6/2)(x + 4/2)
C = (x - 3)(x + 2)
D= 4x²-4x-15
D = (2x)^2 - 2 * 2x * 1 + 1^2 - 1^2 - 15
D = (2x - 1)^2 - 1 - 15
D = (2x - 1)^2 - 16
D = (2x - 1)^2 - 4^2
D = (2x - 1 - 4)(2x - 1 + 4)
D = (2x - 5)(2x + 3)